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Cube Rotation

Tool to list the possible positions of a cube. A die is a cube with 6 differentiated faces, it can be defined by its visible faces so as to know its possible orientations / rotations.

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Cube Rotation -

Tag(s) : Fun/Miscellaneous

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Cube Rotation

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Dice Rotations







Tool to list the possible positions of a cube. A die is a cube with 6 differentiated faces, it can be defined by its visible faces so as to know its possible orientations / rotations.

Answers to Questions

How to list all rotations of the cube?

Place the cube on one side and orient it according to the 4 directions. Move to the next position (other side). And so on.

Example:

-1-
542
-6-
-3-

How to count all possible rotations of a cube?

The die can fall on one of the 6 faces possible and be oriented according to 4 angles, or 24 possibilities. $$ 6 \times 4 = 24 $$

Mathematically, how rotations of a cube are defined?

There are 4 types of rotation:

- Rotation according to the diagonals

- Rotation along the axis connecting the centers of 2 opposite faces

- Rotation along the axis connecting the centers of 2 opposite edges

- Identity rotation (original stationary state)

How to count all possible symmetries of a cube?

A cube whose faces are undifferentiated with 13 axes of symmetries:

- 3 axes pass through the centers of the faces, a cube has 6 faces, so 3 axes

- 6 axes pass through the centers of the opposite edges, a cube has 12 edges, so 6 axes

- 4 axes go through the opposite corners, a cube has 8 angles, so 4 axes

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Source code

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